Q27 of 97 Page 1376

A medicine company has factories at two places, X and Y. From these places, supply is made to each of its three agencies situated at P, Q and R. the monthly requirement of the agencies are respectively 40 packets, 40 packets and 50 packets of medicine, while the production capacity of the factories at X and Y are 60 packets and 70 packets respectively. The transportation costs per packet from the factories to the agencies are given as follows.


How many packets from each factory should be transported to each agency so that the cost of transportation is minimum? Also, find the minimum cost.



Let x packets of medicines be transported from X to P and y packets of medicines be transported from X to Q.


Therefore, 60 - (x + y) will be transported to R.


Also, (40 - x) packets, (40 - y) packets and (50 - (60 - (x + y))) packets will be transported to P, Q, R from Y.


∴According to the question,


x


Minimize Z = 5x + 4(40 - x) + 4y + 2(40 - y) + 3(60 - (x + y)) + 5((x + y) – 10)


Z = 3x + 4y + 370


The feasible region represented by x is given by



The corner points of feasible region are A(0,10) , B(0,40) , C(20,40) , D(40,20), E(10,0).



The minimum value of Z is 40 at point (10,0).


Hence, 10, 0, 50 packets of medicines should be transported from X to P, Q, R and 30, 40, 0 packets of medicines should be transported from Y to P, Q, R.


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A medicine company has factories at two places, X and Y. From these places, supply is made to each of its three agencies situated at P, Q and R. the monthly requirement of the agencies are respectively 40 packets, 40 packets and 50 packets of medicine, while the production capacity of the factories at X and Y are 60 packets and 70 packets respectively. The transportation costs per packet from the factories to the agencies are given as follows.


How many packets from each factory should be transported to each agency so that the cost of transportation is minimum? Also, find the minimum cost.


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An oil company has two depots, A and B, with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three pumps, D, E, F, whose requirements are 4500 L, 3000 L, and 3500 L respectively. The distances (in km) between the depots and the petrol pumps are given in the following table:


Assuming that the transportation cost per km is re 1 per litre, how should the delivery be scheduled in order that the transportation cost is minimum?